Certificate for #13184 ⟨a, b | abb=aaa, bab=ba⟩

Back:⟨a, b | abb=aaa, bab=ba⟩

Completion settings:

[1] abb=aaa

Axiom: abb=aaa.

Defines rule #1.

Referenced by [4], [5], [6].

[2] bab=ba

Axiom: bab=ba.

Defines rule #2.

Referenced by [3], [4], [5].

[3] baab=baa

Overlap of [2] bab=ba with [2] bab=ba:

ba b bab

Critical pair: baba=baab.

Reduce LHS:

[2](bab)a
⇒ baa

Flip LHS and RHS.

Defines rule #4.

[4] aaaab=aaaa

Overlap of [1] abb=aaa with [2] bab=ba:

ab b bab

Critical pair: abba=aaaab.

Reduce LHS:

[1](abb)a
⇒ aaaa

Flip LHS and RHS.

Defines rule #5.

[5] baaa=ba

Overlap of [2] bab=ba with [1] abb=aaa:

b ab abb

Critical pair: baaa=bab.

Reduce RHS:

[2](bab)
⇒ ba

Defines rule #3.

Referenced by [6].

[6] aaaaaa=aaaa

Overlap of [1] abb=aaa with [5] baaa=ba:

ab b baaa

Critical pair: abba=aaaaaa.

Reduce LHS:

[1](abb)a
⇒ aaaa

Flip LHS and RHS.

Defines rule #6.